Not sure where you heard that but that is completely false. BYD alone shipped over 100,000 electric cars (not including buses) in the third quarter (compared to Tesla's 83,000). Other Chinese car companies BAIC, Rowe, and Geel all ship over 20k+ plug-ins per quarter.
Tesla's luxury vehicles ship with 75/90/100kWh packs while BYD's model seem to have 63kWh (not accounting for busses which seems to have about 325kWh). No definite information available for Model 3, afaik, but I heard that the long range version has a 75kWh pack (50kWh for the "normal range" model?).
But yeah I'm not sure whether China doesn't report battery construction, or under reports or what because it sounds suspect to me also.
Official according to who? I suspect that, like much of the less critical reporting on Tesla, it's just reprinting a press release. In any case, that doesn't match the headline; it's just claiming it's the single biggest factory. There's no substantiation of the headline at all, and looking at the numbers it cannot be true.
And you may have noticed how the internet gets, when Tesla/Elon says something that isn't true, so I guess theres some basis to it.
The Tesla fanboyism goes both ways, there are many, many people waiting to point out they are wrong.